You can just refill the tank (standard toilets, I don't know about "tankless" or air-augmented) with a bucket (swimming pool water) and keep using it, after the line pressure drops.

You MUST run a separate circuit or power cords to your gen. Or have a special and expensive cutover system.

Some people think they can make a "double-ended" cord and plug it into a wall socket. Very bad things will happen when the power comes back on and your gen is still plugged in. Not to mention the power company doesn't like their people electrocuted because some yayhoo is feeding power into the line

You can trip the main breakers to isolate, but the best bet is a totally separate circuit to things like refrig and a couple lights.

Note that most gas stoves will not light, even manually, without power. As a safety feature, when the auto-light spark is not functioning the gas will not be released to the burners.

And most electric stoves would draw too much power from a small generator. Just use your barbecue OUTSIDE ONLY!

Also, there is a way you can have Internet access even if all the power is off at the cable and phone companies. Hughesnet (old Direcway) satellite will function fine on a big UPS or gen. I live in So Cal but my service comes from the Maryland Op Center, so the whole darn West Coast could be out and I'd still be on line.

But the service is expensive, about $70/month plus equip costs, and is not very good compared to anybody's DSL or Cable. But if you are REALLY desperate to stay on line, it is one way to go.